I do lots of puzzles and have found if the blade gets slightly loose or stretches the cut may become bowed ands cause this problem of pieces not sliding through both directions. Also when I get heavy handed and start to push into the cut especially when blade gets dull, some blades function better then others, I use mostly pegas, modified geometry #3 and #5 on 3/4 plus thickness. After trying many different blades the pegas modified geometry, # 2/0 for photo puzzles in 1/4 Baltic birch is the only one I use. . I have also learned to be conscious of side pressure into the cut, this causes bowing as well.